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Simplifying 3q2 + -80q + 190 = 0 Reorder the terms: 190 + -80q + 3q2 = 0 Solving 190 + -80q + 3q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 63.33333333 + -26.66666667q + q2 = 0 Move the constant term to the right: Add '-63.33333333' to each side of the equation. 63.33333333 + -26.66666667q + -63.33333333 + q2 = 0 + -63.33333333 Reorder the terms: 63.33333333 + -63.33333333 + -26.66666667q + q2 = 0 + -63.33333333 Combine like terms: 63.33333333 + -63.33333333 = 0.00000000 0.00000000 + -26.66666667q + q2 = 0 + -63.33333333 -26.66666667q + q2 = 0 + -63.33333333 Combine like terms: 0 + -63.33333333 = -63.33333333 -26.66666667q + q2 = -63.33333333 The q term is -26.66666667q. Take half its coefficient (-13.33333334). Square it (177.7777780) and add it to both sides. Add '177.7777780' to each side of the equation. -26.66666667q + 177.7777780 + q2 = -63.33333333 + 177.7777780 Reorder the terms: 177.7777780 + -26.66666667q + q2 = -63.33333333 + 177.7777780 Combine like terms: -63.33333333 + 177.7777780 = 114.44444467 177.7777780 + -26.66666667q + q2 = 114.44444467 Factor a perfect square on the left side: (q + -13.33333334)(q + -13.33333334) = 114.44444467 Calculate the square root of the right side: 10.697871034 Break this problem into two subproblems by setting (q + -13.33333334) equal to 10.697871034 and -10.697871034.Subproblem 1
q + -13.33333334 = 10.697871034 Simplifying q + -13.33333334 = 10.697871034 Reorder the terms: -13.33333334 + q = 10.697871034 Solving -13.33333334 + q = 10.697871034 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '13.33333334' to each side of the equation. -13.33333334 + 13.33333334 + q = 10.697871034 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + q = 10.697871034 + 13.33333334 q = 10.697871034 + 13.33333334 Combine like terms: 10.697871034 + 13.33333334 = 24.031204374 q = 24.031204374 Simplifying q = 24.031204374Subproblem 2
q + -13.33333334 = -10.697871034 Simplifying q + -13.33333334 = -10.697871034 Reorder the terms: -13.33333334 + q = -10.697871034 Solving -13.33333334 + q = -10.697871034 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '13.33333334' to each side of the equation. -13.33333334 + 13.33333334 + q = -10.697871034 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + q = -10.697871034 + 13.33333334 q = -10.697871034 + 13.33333334 Combine like terms: -10.697871034 + 13.33333334 = 2.635462306 q = 2.635462306 Simplifying q = 2.635462306Solution
The solution to the problem is based on the solutions from the subproblems. q = {24.031204374, 2.635462306}
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